SOLUTION: Can someone please, please help me with this problem: Zoro, Inc produces a product that has a variable cost of $6.00 per unit. The company's fixed costs are $30,000. The product

Question 176745: Can someone please, please help me with this problem:
Zoro, Inc produces a product that has a variable cost of $6.00 per unit. The company's fixed costs are $30,000. The product sells for $10.00 a unit and the company desires to earn a $20,000 profit. What is the volume of sales in unit required to achieve the target profit?
a. 5,000
b. 7,500
c. 8,333
d. 12,500
Answer by gonzo(654) (Show Source): You can put this solution on YOUR website!
let p = profit
let r = revenue per unit
let f = fixed cost
let v = variable cost per unit
let x = number of units sold
formula for profit is:
p = r - f - v
p = $20,000
r = x * $10.00
f = $30,000
v = x * $6.00
formula becomes:
$20,000 = (x*$10.00) - $30,000 - (x*$6.00)
add $30,000 to both sides to get:
$50,000 = x*$10.00 - x*$6.00
factor out the x to get:
$50,000 = x * ($10.00 - $6.00)
combine like terms to get:
$50,000 = x * ($4.00)
divide both sides by $4.00 to get:
$50,000 / $4.00 = x
simplify to get:
12,500 = x
looks like the answer is going to be 12,500 units.
substitute in original eqution to see if this holds up.
p = $20,000
r = 12,500 * $10.00 = $125,000
f = $30,000
v = 12,500 * $6.00 = $75,000
formula is:
p = r - f - v
which becomes:
$20,000 = $125,000 - $30,000 - $75,000 = $125,000 - $105,000 = $20,000
equation is true.
answer is:
volume of sales in units required to achieve the target profit is 12,500 units.
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